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For questions about short exact sequences in various contexts, including questions on short exact sequences of groups or modules.

4 votes
0 answers
113 views

How can one characterize categories of exact functors?

Does there exist any intrinsic characterization of additive categories equivalent to $\operatorname{Ex}(A,Ab)$, that is, of exact functors from a small abelian category $A$ into abelian groups? Any hi …
Mikhail Bondarko's user avatar
1 vote
0 answers
70 views

On (universal) additive functors making a given complex contractible: examples?

Let $M=(M^i)$ be a (cohomological) complex of objects of some additive category $A$ (I am mostly interested in "short" complexes; yet one may also consider an unbounded $M$). I am interested in those …
Mikhail Bondarko's user avatar
11 votes
Accepted

Does the Grothendieck group depend on the embedding?

I think that the Grothendieck group DOES depend on A. Indeed, any additive category C could be embedded (by the Yoneda embedding) into the abelian category of contravariant additive functors from C to …
Mikhail Bondarko's user avatar